1 Decision Model for Agroforestry Insurance

Decision Analysis (DA) can be used to support practical decisions in agroforestry insurance design under risk and uncertainty. It can generate robust and science-based decision support by integrating data and expert knowledge on insurance mechanisms and their impacts on agroforestry systems. We demonstrate DA model development techniques to support the difficult task of deciding which insurance schemes to implement, given the complex nature of agroforestry risks and farmer perceptions.

The decisionSupport() function is part of the package decisionSupport in the R programming environment. This package was used for a Monte-Carlo-based selection of optimal insurance strategies.

1.1 Model Structure

By coding a participatory conceptual model as a Monte Carlo simulation using the decisionSupport() function, we were able to offer decision makers probable outcomes in terms of Net Present Value (NPV) and assess the resilience benefits of different insurance schemes for agroforestry systems.

Participatory conceptual model of agroforestry insurance
Participatory conceptual model of agroforestry insurance

1.2 Input Table

The input table Agroforestry_insurance_input_table.csv contains the variables used in the model with distributions described by a 90% confidence interval, as well as the shape of the distribution.

Table of expert estimates for agroforestry insurance model variables
variable lower median upper distribution label
n_years 10.000 10.00 const Project timeline in years
var_CV 5.000 20.00 posnorm Coefficient of variation for time series
index_trigger_threshold 0.200 0.40 tnorm_0_1 Damage level that triggers index insurance
if_subsidy_available 0.200 0.40 tnorm_0_1 Prob that a subsidy is available
tree_value_per_ha 1000.000 5000.00 posnorm Value of trees per hectare
crop_value_per_ha 500.000 2000.00 posnorm Value of crops per hectare
af_system_size 0.500 5.00 posnorm Agroforestry system size in hectares
annual_income_per_ha 800.000 2000.00 posnorm Annual farm income (USD/ha/year)
typhoon_probability 0.100 0.30 tnorm_0_1 Annual probability of typhoon
typhoon_loss_rate 0.200 0.80 tnorm_0_1 Loss percentage when typhoon occurs
savings_per_ha 100.000 500.00 posnorm Available savings (USD/ha)
aid_expectation 0.010 0.20 tnorm_0_1 Prob that aid is available after a typhoon
aid_per_ha 50.000 200.00 posnorm Expected aid after typhoon (USD/ha)
premium_index_per_ha 20.000 80.00 posnorm Index insurance premium (USD/ha/year)
premium_traditional_per_ha 30.000 100.00 posnorm Traditional premium (USD/ha/year)
premium_hybrid_per_ha 25.000 90.00 posnorm Hybrid premium (USD/ha/year)
subsidy_probability 0.300 0.80 tnorm_0_1 Probability subsidy available
subsidy_level 0.400 0.70 tnorm_0_1 Subsidy percentage if available
farm_size_ha 1.000 5.00 posnorm Farm size in hectares
max_payout_index 0.600 0.90 tnorm_0_1 Maximum payout as percentage of loss for index insurance
max_payout_traditional 0.700 0.95 tnorm_0_1 Maximum payout as percentage of loss for traditional insurance
hybrid_index_share 0.300 0.55 tnorm_0_1 Index payout for hybrid insurance scheme
claims_processing_rate 0.030 0.08 tnorm_0_1 Administrative cost as percentage of payout
basis_risk 0.100 0.40 tnorm_0_1 Risk that index doesn’t match actual losses
practice_risk_reduction 0.100 0.40 tnorm_0_1 Risk reduction from good practices for risk-adjusted premiums
farmer_discount_rate 3.000 8.00 posnorm Discount rate for farmer perspective (%)
social_discount_rate 1.000 5.00 posnorm Discount rate for social perspective (%)
base_premium_index 1.000 5.00 posnorm Base premium rate for index insurance (%)
base_premium_traditional 3.000 8.00 posnorm Base premium rate for traditional insurance (%)
base_premium_hybrid 2.000 6.00 posnorm Base premium rate for hybrid insurance (%)
admin_costs_index 5000.000 20000.00 posnorm Annual admin costs for index insurance
admin_costs_traditional 8000.000 25000.00 posnorm Annual admin costs for traditional insurance
admin_costs_hybrid 6000.000 18000.00 posnorm Annual admin costs for hybrid insurance
claims_history 0.001 3.00 posnorm Number of past claims (last 3 years)
loss_ratio 0.500 1.20 posnorm Historical loss ratio
credibility_factor 0.300 0.80 tnorm_0_1 Weight given to farm experience
catastrophe_load 0.100 0.30 tnorm_0_1 Catastrophe risk loading
pool_loss_ratio 0.600 0.90 tnorm_0_1 Average loss ratio for similar farms
self_insurance_costs 2000.000 8000.00 posnorm Costs of self-insurance alternatives
alternative_investment_returns 1000.000 5000.00 posnorm Returns from alternative investments
risk_reduction_value 1000.000 3000.00 posnorm Value of risk reduction benefits
management_improvement_value 500.000 2500.00 posnorm Value of improved management practices
damage_assessment_accuracy 0.600 0.95 tnorm_0_1 Accuracy of damage assessment
participatory 1.000 5.00 posnorm Level of stakeholder involvement in insurance design
neutral 1.000 5.00 posnorm Impartiality in decision-making processes
farmers_understand_insurance 1.000 5.00 posnorm Farmer comprehension of insurance terms and benefits
just 1.000 5.00 posnorm Fairness and ethical considerations in insurance design
coverage_cultural_value 1.000 5.00 posnorm Insurance accounts for cultural significance of risks
equity 1.000 5.00 posnorm Fair distribution of benefits and costs
time_to_adjust 1.000 5.00 posnorm Time needed for adaptation to new conditions
resources_to_cope 1.000 5.00 posnorm Availability of cash, extension services, seeds
other_important_risks 1.000 5.00 posnorm Presence of risks more critical than insured ones
fairness 1.000 5.00 posnorm Overall fairness of insurance scheme
af_multiple_stages 1.000 5.00 posnorm Agroforestry systems with multiple growth stages
diversity_of_group 1.000 5.00 posnorm Variety of stakeholders sharing risks
transferability_risk 1.000 5.00 posnorm Ability to transfer risk to third parties
redundancy_actors 1.000 5.00 posnorm Backup systems and multiple service providers
factors_resilience 1.000 5.00 posnorm Ecological and social resilience factors
sustainability_insurance 1.000 5.00 posnorm Long-term viability of insurance scheme
ability_continue_farming 1.000 5.00 posnorm Farmers’ capacity to maintain operations
farm_resilience 1.000 5.00 posnorm Farm system ability to withstand shocks
economically_sustainable 1.000 5.00 posnorm Financial viability for insurers
farmers_subscribe 1.000 5.00 posnorm Insurance uptake rate among farmers
pay_out 1.000 5.00 posnorm Compensation payment mechanisms
climate_justice 1.000 5.00 posnorm Insurance as climate justice instrument
affordability_premium 1.000 5.00 posnorm Premium cost relative to farmer income
level_micro_meso_macro 1.000 5.00 posnorm Scale of insurance implementation
damage_assessment 1.000 5.00 posnorm Accuracy and fairness of loss assessment
new_adaptation_strategies 1.000 5.00 posnorm Development of innovative adaptation methods
spatial_geophysical 1.000 5.00 posnorm Topography and physical landscape features
af_profile 1.000 5.00 posnorm Diversity and size of agroforestry systems
socio_political 1.000 5.00 posnorm Political stability and governance context
availability_insurance 1.000 5.00 posnorm Accessibility of insurance products
cohesiveness_community 1.000 5.00 posnorm Social unity and collective action
cultural_importance 1.000 5.00 posnorm Cultural significance of insured assets
risk_perception 1.000 5.00 posnorm Subjective assessment of risk severity
vulnerability 1.000 5.00 posnorm Susceptibility to climate impacts
number_insured 1.000 5.00 posnorm Total participants in insurance scheme
exposure_risks 1.000 5.00 posnorm Degree of exposure to climate hazards
underwriting 1.000 5.00 posnorm Risk assessment and premium setting
risk_mitigating_practices 1.000 5.00 posnorm Adoption of risk reduction measures
damage 1.000 5.00 posnorm Extent of losses from climate events
hazard 1.000 5.00 posnorm Frequency and severity of climate hazards
what_is_insured 1.000 5.00 posnorm Scope of insurance coverage
financing 1.000 5.00 posnorm Funding sources and mechanisms
farmer_pays 1.000 5.00 posnorm Farmer contribution to premiums
subsidized 1.000 5.00 posnorm Level of government or donor subsidies
ease_claims 1.000 5.00 posnorm Simplicity of claims process
indemnity_index 1.000 5.00 posnorm Basis for compensation calculations
ease_getting_insurance 1.000 5.00 posnorm Accessibility of enrollment process
ecological_conditions 1.000 5.00 posnorm Environmental and climate factors
composition_insured 1.000 5.00 posnorm Demographics of insured population
insurance_offered 1.000 5.00 posnorm Types of insurance products available
decision 1.000 5.00 posnorm Quality of decision-making processes
land_tenure 1.000 5.00 posnorm Security of land ownership and access
design_process 1.000 5.00 posnorm Inclusivity of scheme design
compliance_mechanism 1.000 5.00 posnorm Enforcement of insurance terms
time_frame_policy 1.000 5.00 posnorm Duration of policy coverage
gendered_decision_making 1.000 5.00 posnorm Gender equity in decision-making
likelihood_extreme_events 1.000 5.00 posnorm Probability of severe climate events
personal_savings_coverage 1.000 5.00 posnorm Adequacy of personal risk management
external_influences 1.000 5.00 posnorm Impact of external factors on decisions
past_experiences_damages 1.000 5.00 posnorm Historical loss experiences
cultural_acceptance 1.000 5.00 posnorm Social norms regarding insurance
expected_compensation 1.000 5.00 posnorm Perceived benefits from insurance
dependence_insured_risk 1.000 5.00 posnorm Economic reliance on insured assets
trust_insurers_farmers 1.000 5.00 posnorm Confidence in insurance providers
portfolio_risk_management 1.000 5.00 posnorm Diversity of risk strategies
uptake_insurance 1.000 5.00 posnorm Actual adoption rates
data_availability 1.000 5.00 posnorm Access to relevant risk data
motivations 1.000 5.00 posnorm Drivers for insurance participation
feasibility_insurance 1.000 5.00 posnorm Practical implementation potential

1.3 Key Risk Categories in Agroforestry

1.3.1 Production Risks

  • Climate variability and extreme weather events
  • Pest and disease outbreaks
  • Yield fluctuations across multiple species
  • Tree-crop interactions and competition
  • Long-term tree establishment risks

1.3.2 Market Risks

  • Price volatility for multiple products
  • Market access limitations
  • Input cost fluctuations
  • Value chain disruptions

1.3.3 Institutional Risks

  • Policy changes affecting agroforestry
  • Land tenure security
  • Access to credit and insurance markets

1.4 Insurance Scheme Options

1.4.1 Index-Based Insurance

  • Weather index insurance
  • Yield index insurance
  • Area-based yield indices
  • Satellite vegetation indices

1.4.2 Traditional Insurance

  • Multi-peril crop insurance
  • Named-peril insurance
  • Revenue protection insurance
  • Whole-farm revenue insurance

1.5 Model Implementation

The decision model evaluates the net benefits of different insurance schemes for agroforestry systems, considering:

  1. Premium costs and administrative expenses
  2. Payout probabilities and amounts
  3. Risk reduction benefits
  4. Behavioral impacts on farm management
  5. Systemic risk factors
# Source our model
source("AF_Insurance_model.R")

# Ensure consistent results with the random number generator
# not for each 'run' of the MC simulation but for 
# consistency each time we run the entire simulation 
set.seed(42)

agroforestry_insurance_simulation_results <- mcSimulation(
  estimate = estimate_read_csv("data/Agroforestry_insurance_input_table.csv"),
  model_function = agroforestry_insurance_function,
  numberOfModelRuns = 1e4, #run 10,000 times
  functionSyntax = "plainNames"
)

The Net Present Value (i.e. current value of the future benefits) of the garden decision options over 10 years of the insurance scheme intervention.

1.6 Results and Decision Support

The model provides probabilistic outcomes for each insurance scheme, allowing decision-makers to:

  • Compare expected net benefits across options
  • Assess risk-return tradeoffs
  • Identify critical uncertainties
  • Develop robust insurance strategies
# NPV is USD total net benefit over the project period 
plot_distributions(mcSimulation_object = agroforestry_insurance_simulation_results, 
                   vars = c("NPV_index_farmer", "NPV_traditional_farmer", "NPV_hybrid_farmer"),
                   old_names = c("NPV_index_farmer", "NPV_traditional_farmer", "NPV_hybrid_farmer"),
                   new_names = c("Index-based insurance NPV","Traditional insurance NPV", "Hybrid insurance NPV"),
                                    method = "boxplot", 
                                    base_size = 11, 
                                    x_axis_name = "Net Present Value (NPV) farmer perspective (USD over the project period)")

ggsave("figures/NPV_Boxplots_Farmer.png", width = 15, height = 8, units = "cm")
# NPV is USD total net benefit over the project period 
plot_distributions(mcSimulation_object = agroforestry_insurance_simulation_results, 
                   vars = c("NPV_index_social", 
                             "NPV_traditional_social",
                             "NPV_hybrid_social"),
                   old_names = c( "NPV_index_social", 
                             "NPV_traditional_social",
                             "NPV_hybrid_social"),
                   new_names = c("Index-based insurance NPV",
                                 "Traditional insurance NPV", 
                                 "Hybrid insurance NPV"),
                                    method = "boxplot", 
                                    base_size = 11, 
                                    x_axis_name = "Net Present Value (NPV) society perspective (USD over the project period)")

ggsave("figures/NPV_Boxplots_Social.png", width = 15, height = 8, units = "cm")
# NPV is USD total net benefit over the project period 
plot_distributions(mcSimulation_object = agroforestry_insurance_simulation_results, 
                   vars = c("NPV_index_insurer", 
                            "NPV_traditional_insurer", 
                            "NPV_hybrid_insurer"),
                   old_names = c("NPV_index_insurer", 
                            "NPV_traditional_insurer", 
                            "NPV_hybrid_insurer"),
                   new_names = c("Index-based insurance NPV",
                                 "Traditional insurance NPV", 
                                 "Hybrid insurance NPV"),
                                    method = "boxplot", 
                                    base_size = 11, 
                                    x_axis_name = "Net Present Value (NPV) insurer perspective (USD over the project period)")

ggsave("figures/NPV_Boxplots_Insurer.png", width = 15, height = 8, units = "cm")

1.7 Conclusion

This decision support model provides a structured approach to evaluating agroforestry insurance schemes, helping to bridge the gap between traditional risk management and the unique challenges of diversified agroforestry systems.